Storage systems are often configured to include multiple storage tiers, with different ones of the tiers providing different levels of input-output (IO) performance or other characteristics. In such systems, data may be moved from one tier to another within a given storage system based on access frequency of the data or other factors. However, conventional storage tiering arrangements in many contexts can lead to excessive power consumption. For example, in supercomputers and other types of high-performance computer systems that perform computations using hundreds or thousands of compute nodes, excessive storage system power consumption can unduly limit the achievable levels of computational performance.